1. Field of the Invention
The present invention relates to a multi-wavelength interferometer, a measurement apparatus, and a measurement method.
2. Description of the Related Art
A heterodyne interferometric method has been generally known as an apparatus for accurately measuring the shape of a measurement surface. In a single-wavelength interferometer (refer to Japanese Patent Application Laid-Open No. 10-185529), if a measurement surface is rough, a speckle pattern resulting from surface roughness has a random phase with a standard deviation larger than 2π to increase inaccuracy in measurement, making it difficult to perform an accurate measurement.
Japanese Patent Application Laid-Open No. 05-71918 discusses a method for solving the above problem, in which, in an apparatus for irradiating an object surface with a laser beam to image reflected light, the position of a diaphragm of an imaging lens is varied to incoherently average a random phase of a speckle pattern.
As another solving method, a multi-wavelength interferometer has been known in which the phases of wavelengths are combined based on the result of interference measurement on a plurality of different wavelengths (refer to Document 1: A. F. Fercher, et al. “Rough-surface interferometry with a two-wavelength heterodyne speckle interferometer,” Applied Optics, 1985, vol. 24, issue 14, pp 2181-2188). According to Document 1, if the speckles of two wavelengths are correlative with each other, information is acquired about a macroscopic surface profile and a microscopic surface roughness based on a difference in phase between the two wavelengths.
It has been known that the correlation of a speckle pattern between the two wavelengths depends on a wavelength in which the two wavelengths are combined (refer to Document 2: U. Vry and F. Fercher, “High-order statistical properties of speckle fields and their application to rough-surface interferometry,” J. Opt. Soc. Am. A, 1986, vol. 3, issue 7, pp 988-1000). It is assumed that the more coincident the two speckle patterns, the higher the degree of correlation. According to Document 2, the smaller a composite wavelength Λ, the less the correlation of the speckle pattern between the two wavelengths. On the other hand, the greater the composite wavelength Λ, the more the correlation of the speckle pattern between the two wavelengths. The term “composite wavelength Λ” refers to a quantity represented by Λ=λ1×λ2/(λ1−λ2), where the two wavelengths are λ1 and λ2 (λ1>λ2). Thus, the multi-wavelength interferometer is capable of accurately measuring a rough measurement surface, which is difficult for the single-wavelength interferometer to measure.
According to Document 2, the correlation of the speckle pattern between the two wavelengths depends on the magnitude of the composite wavelength, the roughness of the measurement surface, and the inclination of the measurement surface (refer to numerical expression (1)).
                    μ        =                              exp            ⁡                          (                                                                    4                    ⁢                    πⅈ                                    Λ                                ⁢                                  h                  0                                            )                                ×                      exp            [                                          -                                                      4                    ⁢                                          π                      2                                                                            Λ                    2                                                              ⁢                              (                                                      2                    ⁢                                          σ                      h                      2                                                        +                                                            s                      2                                        ⁢                                          a                      2                                                                      )                                      ]                                              (        1        )            where, “μ” represents a complex correlation between two wavelengths, “h0” represents the height of the measurement surface, and “Λ” represents the composite wavelength of two wavelengths. “σh” represents the roughness of the measurement surface, “s” represents the inclination of the measurement surface, and “a” represents diameter in irradiating the measurement surface with Gaussian beam.
According to numerical expression (1), the greater the roughness of the measurement surface, the lower the correlation of the speckle between the two wavelengths. The greater the inclination of the measurement surface, the lower the correlation of the speckle between the two wavelengths. In particular, the inclination of the measurement surface greatly affects a reduction in the correlation of the speckle between the two wavelengths.
FIG. 1 illustrates a relationship between the inclination angle of the measurement surface and a length measurement error. FIG. 1 indicates the result of simulation of the length measurement error in a case where the measurement surface with a roughness Ra of 0.4 μm is illuminated with beam of 65 μm spot size and measurement is performed by a two-wavelength interferometer with a composite wavelength of 300 μm which receives light in a range of a numerical aperture (NA) of 0.02. The term “length measurement error” refers to a value of 2σ of length measurement of 100 samples of the measurement surfaces.
According to FIG. 1, at the inclination angle of the measurement surface of 0°, the length measurement error is as small as 0.6 μm. However, at the inclination angle of the measurement surface of 10°, the length measurement error is significantly deteriorated, as poor as 8.1 μm.
In general, the speckle pattern on the pupil conjugate plane of the measurement surface (a plane relative to Fourier transform) in a case where a rough measurement surface inclines is formed as such a pattern that a speckle pattern in a case where a measurement surface does not incline is shifted (lateral shift) in a pupil surface. If the rough measurement surface inclines, a difference occurs in shift amount of the speckle pattern in the pupil surface between different wavelengths λ1 and λ2 formed on the pupil conjugate plane of the measurement surface, so that the correlation of the speckle pattern between two wavelengths decreases to deteriorate the accuracy of length measurement. The greater the inclination angle of the measurement surface, the larger the difference in shift amount of the speckle pattern in the pupil surface between the wavelengths, so that the correlation of the speckle pattern between two wavelengths is further decreased to cause significant deterioration of a length measurement accuracy. Thus, even though a multi-wavelength interferometer is applied to measure a rough surface, the inclination of the measurement surface decreases a correlation between wavelengths, which makes accurate measurement difficult.